Questioning MLE for the estimation of environmental extreme distributions
Résumé
In determining extreme environmental variables, such as wave heights, with the Peaks-Over-Threshold (POT) method, it has become common practice in the metocean community to use the GPD–Poisson model fitted by the Maximum Likelihood Estimator (MLE). However, Mazas and Hamm (2011) pointed out some difficulties in getting stable estimations of extreme quantiles with this method. Further investigation reported in the present paper enable to understand that this problem is linked to the behavior of the likelihood function and to solve it by introducing a location parameter and replacing maximum likelihood estimated two-parameter distributions by L-moments estimated three-parameter distributions. Applications on real and simulated data highlight the distinction between the location parameter of a statistical distribution and the statistical threshold chosen in the POT context. With three-parameter distributions, MLE is no more suitable and it is found that the L-moments estimator can be a valid alternative. With these two improvements, stable quantiles are obtained not only with the GPD but also with other distributions such as Weibull and Gamma (Pearson-III).